Question: Divide the following complex numbers: $\dfrac{8 e^{4\pi i / 3}}{2 e^{7\pi i / 12}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Answer: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $8 e^{4\pi i / 3}$ ) has angle $\frac{4}{3}\pi$ and radius 8. The second number ( $2 e^{7\pi i / 12}$ ) has angle $\frac{7}{12}\pi$ and radius 2. The radius of the result will be $\frac{8}{2}$ , which is 4. The angle of the result is $\frac{4}{3}\pi - \frac{7}{12}\pi = \frac{3}{4}\pi$ The radius of the result is $4$ and the angle of the result is $\frac{3}{4}\pi$.